Question

X^2+2x+1 is a perfect square trinomial True of False?

Answer 1

Answer:

True.

Step-by-step explanation:

It is because it is in the form $a^2x^2+2abx+b^2$ and this equals $(ax+b)^2$.

Why it is in that form:  well comparing  $a^2x^2+2abx+b^2$, we have $a=1, b=1$. Testing, plug in those values:

$(1)^2x^2+2(1)(1)x+(1)^2$

$1x^2+2x+1$

$x^2+2x+1$.

This has the squared form of $(x+1)^2$.

Test if you like:

$(x+1)^2$

$(x+1)(x+1)$

Use foil to expand:

First: x(x)=x^2

Outer: x(1)=x

Inner: 1(x)=x

Last: 1(1)=1

---------------Add together

$x^2+2x+1$

It does indeed equal.